LMFDB - Embedded newform 8041.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.67122 q^{2} +2.62074 q^{3} +5.13539 q^{4} +0.949400 q^{5} -7.00056 q^{6} -4.03564 q^{7} -8.37532 q^{8} +3.86827 q^{9} +O(q^{10})$	\(q-2.67122 q^{2} +2.62074 q^{3} +5.13539 q^{4} +0.949400 q^{5} -7.00056 q^{6} -4.03564 q^{7} -8.37532 q^{8} +3.86827 q^{9} -2.53605 q^{10} -1.00000 q^{11} +13.4585 q^{12} +0.167776 q^{13} +10.7801 q^{14} +2.48813 q^{15} +12.1015 q^{16} +1.00000 q^{17} -10.3330 q^{18} -8.43016 q^{19} +4.87554 q^{20} -10.5764 q^{21} +2.67122 q^{22} +5.22814 q^{23} -21.9495 q^{24} -4.09864 q^{25} -0.448166 q^{26} +2.27550 q^{27} -20.7246 q^{28} +8.85167 q^{29} -6.64633 q^{30} +5.94666 q^{31} -15.5751 q^{32} -2.62074 q^{33} -2.67122 q^{34} -3.83144 q^{35} +19.8651 q^{36} +5.66287 q^{37} +22.5188 q^{38} +0.439697 q^{39} -7.95152 q^{40} -1.71029 q^{41} +28.2517 q^{42} +1.00000 q^{43} -5.13539 q^{44} +3.67253 q^{45} -13.9655 q^{46} +2.40992 q^{47} +31.7148 q^{48} +9.28639 q^{49} +10.9484 q^{50} +2.62074 q^{51} +0.861596 q^{52} -7.83596 q^{53} -6.07835 q^{54} -0.949400 q^{55} +33.7998 q^{56} -22.0932 q^{57} -23.6447 q^{58} -9.07751 q^{59} +12.7775 q^{60} +6.13333 q^{61} -15.8848 q^{62} -15.6109 q^{63} +17.4014 q^{64} +0.159287 q^{65} +7.00056 q^{66} -4.24323 q^{67} +5.13539 q^{68} +13.7016 q^{69} +10.2346 q^{70} -11.5783 q^{71} -32.3980 q^{72} +4.99497 q^{73} -15.1267 q^{74} -10.7415 q^{75} -43.2922 q^{76} +4.03564 q^{77} -1.17453 q^{78} +4.03713 q^{79} +11.4892 q^{80} -5.64131 q^{81} +4.56855 q^{82} -7.69890 q^{83} -54.3137 q^{84} +0.949400 q^{85} -2.67122 q^{86} +23.1979 q^{87} +8.37532 q^{88} +3.38193 q^{89} -9.81013 q^{90} -0.677084 q^{91} +26.8486 q^{92} +15.5846 q^{93} -6.43741 q^{94} -8.00359 q^{95} -40.8181 q^{96} -6.26604 q^{97} -24.8059 q^{98} -3.86827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) $ 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.67122	−1.88883	−0.944417	−	0.328749i	$-0.893373\pi$
$2$	−2.67122	−1.88883	−0.944417	+	0.328749i	$0.893373\pi$
$3$	2.62074	1.51308	0.756542	−	0.653945i	$-0.226887\pi$
$3$	2.62074	1.51308	0.756542	+	0.653945i	$0.226887\pi$
$4$	5.13539	2.56770
$5$	0.949400	0.424585	0.212292	−	0.977206i	$-0.431907\pi$
$5$	0.949400	0.424585	0.212292	+	0.977206i	$0.431907\pi$
$6$	−7.00056	−2.85797
$7$	−4.03564	−1.52533	−0.762664	−	0.646795i	$-0.776109\pi$
$7$	−4.03564	−1.52533	−0.762664	+	0.646795i	$0.776109\pi$
$8$	−8.37532	−2.96112
$9$	3.86827	1.28942
$10$	−2.53605	−0.801970
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	13.4585	3.88514
$13$	0.167776	0.0465327	0.0232664	−	0.999729i	$-0.492593\pi$
$13$	0.167776	0.0465327	0.0232664	+	0.999729i	$0.492593\pi$
$14$	10.7801	2.88109
$15$	2.48813	0.642432
$16$	12.1015	3.02537
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−10.3330	−2.43551
$19$	−8.43016	−1.93401	−0.967006	−	0.254755i	$-0.918005\pi$
$19$	−8.43016	−1.93401	−0.967006	+	0.254755i	$0.918005\pi$
$20$	4.87554	1.09020
$21$	−10.5764	−2.30795
$22$	2.67122	0.569505
$23$	5.22814	1.09014	0.545072	−	0.838389i	$-0.316502\pi$
$23$	5.22814	1.09014	0.545072	+	0.838389i	$0.316502\pi$
$24$	−21.9495	−4.48042
$25$	−4.09864	−0.819728
$26$	−0.448166	−0.0878926
$27$	2.27550	0.437920
$28$	−20.7246	−3.91658
$29$	8.85167	1.64371	0.821857	−	0.569694i	$-0.192938\pi$
$29$	8.85167	1.64371	0.821857	+	0.569694i	$0.192938\pi$
$30$	−6.64633	−1.21345
$31$	5.94666	1.06805	0.534026	−	0.845468i	$-0.320678\pi$
$31$	5.94666	1.06805	0.534026	+	0.845468i	$0.320678\pi$
$32$	−15.5751	−2.75331
$33$	−2.62074	−0.456212
$34$	−2.67122	−0.458110
$35$	−3.83144	−0.647631
$36$	19.8651	3.31085
$37$	5.66287	0.930970	0.465485	−	0.885056i	$-0.345880\pi$
$37$	5.66287	0.930970	0.465485	+	0.885056i	$0.345880\pi$
$38$	22.5188	3.65303
$39$	0.439697	0.0704079
$40$	−7.95152	−1.25725
$41$	−1.71029	−0.267102	−0.133551	−	0.991042i	$-0.542638\pi$
$41$	−1.71029	−0.267102	−0.133551	+	0.991042i	$0.542638\pi$
$42$	28.2517	4.35934
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−5.13539	−0.774190
$45$	3.67253	0.547469
$46$	−13.9655	−2.05910
$47$	2.40992	0.351523	0.175761	−	0.984433i	$-0.443761\pi$
$47$	2.40992	0.351523	0.175761	+	0.984433i	$0.443761\pi$
$48$	31.7148	4.57764
$49$	9.28639	1.32663
$50$	10.9484	1.54833
$51$	2.62074	0.366977
$52$	0.861596	0.119482
$53$	−7.83596	−1.07635	−0.538176	−	0.842833i	$-0.680886\pi$
$53$	−7.83596	−1.07635	−0.538176	+	0.842833i	$0.680886\pi$
$54$	−6.07835	−0.827159
$55$	−0.949400	−0.128017
$56$	33.7998	4.51668
$57$	−22.0932	−2.92632
$58$	−23.6447	−3.10470
$59$	−9.07751	−1.18179	−0.590896	−	0.806748i	$-0.701225\pi$
$59$	−9.07751	−1.18179	−0.590896	+	0.806748i	$0.701225\pi$
$60$	12.7775	1.64957
$61$	6.13333	0.785293	0.392646	−	0.919690i	$-0.371560\pi$
$61$	6.13333	0.785293	0.392646	+	0.919690i	$0.371560\pi$
$62$	−15.8848	−2.01737
$63$	−15.6109	−1.96679
$64$	17.4014	2.17517
$65$	0.159287	0.0197571
$66$	7.00056	0.861709
$67$	−4.24323	−0.518393	−0.259196	−	0.965825i	$-0.583458\pi$
$67$	−4.24323	−0.518393	−0.259196	+	0.965825i	$0.583458\pi$
$68$	5.13539	0.622758
$69$	13.7016	1.64948
$70$	10.2346	1.22327
$71$	−11.5783	−1.37409	−0.687043	−	0.726616i	$-0.741092\pi$
$71$	−11.5783	−1.37409	−0.687043	+	0.726616i	$0.741092\pi$
$72$	−32.3980	−3.81814
$73$	4.99497	0.584617	0.292308	−	0.956324i	$-0.405577\pi$
$73$	4.99497	0.584617	0.292308	+	0.956324i	$0.405577\pi$
$74$	−15.1267	−1.75845
$75$	−10.7415	−1.24032
$76$	−43.2922	−4.96595
$77$	4.03564	0.459904
$78$	−1.17453	−0.132989
$79$	4.03713	0.454212	0.227106	−	0.973870i	$-0.427074\pi$
$79$	4.03713	0.454212	0.227106	+	0.973870i	$0.427074\pi$
$80$	11.4892	1.28453
$81$	−5.64131	−0.626813
$82$	4.56855	0.504512
$83$	−7.69890	−0.845064	−0.422532	−	0.906348i	$-0.638859\pi$
$83$	−7.69890	−0.845064	−0.422532	+	0.906348i	$0.638859\pi$
$84$	−54.3137	−5.92612
$85$	0.949400	0.102977
$86$	−2.67122	−0.288045
$87$	23.1979	2.48708
$88$	8.37532	0.892812
$89$	3.38193	0.358484	0.179242	−	0.983805i	$-0.442636\pi$
$89$	3.38193	0.358484	0.179242	+	0.983805i	$0.442636\pi$
$90$	−9.81013	−1.03408
$91$	−0.677084	−0.0709777
$92$	26.8486	2.79916
$93$	15.5846	1.61605
$94$	−6.43741	−0.663968
$95$	−8.00359	−0.821151
$96$	−40.8181	−4.16598
$97$	−6.26604	−0.636220	−0.318110	−	0.948054i	$-0.603048\pi$
$97$	−6.26604	−0.636220	−0.318110	+	0.948054i	$0.603048\pi$
$98$	−24.8059	−2.50578
$99$	−3.86827	−0.388775
$100$	−21.0481	−2.10481
$101$	13.5038	1.34367	0.671837	−	0.740699i	$-0.265505\pi$
$101$	13.5038	1.34367	0.671837	+	0.740699i	$0.265505\pi$
$102$	−7.00056	−0.693158
$103$	−19.6363	−1.93482	−0.967410	−	0.253215i	$-0.918512\pi$
$103$	−19.6363	−1.93482	−0.967410	+	0.253215i	$0.918512\pi$
$104$	−1.40518	−0.137789
$105$	−10.0412	−0.979920
$106$	20.9315	2.03305
$107$	15.0067	1.45075	0.725374	−	0.688355i	$-0.241667\pi$
$107$	15.0067	1.45075	0.725374	+	0.688355i	$0.241667\pi$
$108$	11.6856	1.12445
$109$	−18.2609	−1.74907	−0.874537	−	0.484958i	$-0.838835\pi$
$109$	−18.2609	−1.74907	−0.874537	+	0.484958i	$0.838835\pi$
$110$	2.53605	0.241803
$111$	14.8409	1.40864
$112$	−48.8372	−4.61468
$113$	−0.831552	−0.0782258	−0.0391129	−	0.999235i	$-0.512453\pi$
$113$	−0.831552	−0.0782258	−0.0391129	+	0.999235i	$0.512453\pi$
$114$	59.0158	5.52734
$115$	4.96360	0.462858
$116$	45.4568	4.22056
$117$	0.649003	0.0600003
$118$	24.2480	2.23221
$119$	−4.03564	−0.369946
$120$	−20.8389	−1.90232
$121$	1.00000	0.0909091
$122$	−16.3835	−1.48329
$123$	−4.48222	−0.404148
$124$	30.5385	2.74243
$125$	−8.63825	−0.772628
$126$	41.7002	3.71495
$127$	10.0286	0.889894	0.444947	−	0.895557i	$-0.353222\pi$
$127$	10.0286	0.889894	0.444947	+	0.895557i	$0.353222\pi$
$128$	−15.3327	−1.35523
$129$	2.62074	0.230743
$130$	−0.425489	−0.0373179
$131$	−18.2205	−1.59194	−0.795968	−	0.605339i	$-0.793038\pi$
$131$	−18.2205	−1.59194	−0.795968	+	0.605339i	$0.793038\pi$
$132$	−13.4585	−1.17141
$133$	34.0211	2.95000
$134$	11.3346	0.979158
$135$	2.16036	0.185934
$136$	−8.37532	−0.718177
$137$	−0.803989	−0.0686894	−0.0343447	−	0.999410i	$-0.510934\pi$
$137$	−0.803989	−0.0686894	−0.0343447	+	0.999410i	$0.510934\pi$
$138$	−36.5999	−3.11559
$139$	−18.8259	−1.59679	−0.798397	−	0.602132i	$-0.794318\pi$
$139$	−18.8259	−1.59679	−0.798397	+	0.602132i	$0.794318\pi$
$140$	−19.6759	−1.66292
$141$	6.31576	0.531883
$142$	30.9280	2.59542
$143$	−0.167776	−0.0140301
$144$	46.8118	3.90098
$145$	8.40377	0.697895
$146$	−13.3426	−1.10424
$147$	24.3372	2.00730
$148$	29.0811	2.39045
$149$	21.8999	1.79411	0.897053	−	0.441922i	$-0.145703\pi$
$149$	21.8999	1.79411	0.897053	+	0.441922i	$0.145703\pi$
$150$	28.6928	2.34275
$151$	−9.65566	−0.785766	−0.392883	−	0.919588i	$-0.628522\pi$
$151$	−9.65566	−0.785766	−0.392883	+	0.919588i	$0.628522\pi$
$152$	70.6052	5.72684
$153$	3.86827	0.312731
$154$	−10.7801	−0.868682
$155$	5.64576	0.453479
$156$	2.25802	0.180786
$157$	16.0423	1.28031	0.640156	−	0.768245i	$-0.278870\pi$
$157$	16.0423	1.28031	0.640156	+	0.768245i	$0.278870\pi$
$158$	−10.7840	−0.857932
$159$	−20.5360	−1.62861
$160$	−14.7870	−1.16901
$161$	−21.0989	−1.66283
$162$	15.0692	1.18395
$163$	15.6179	1.22329	0.611643	−	0.791134i	$-0.290509\pi$
$163$	15.6179	1.22329	0.611643	+	0.791134i	$0.290509\pi$
$164$	−8.78301	−0.685838
$165$	−2.48813	−0.193701
$166$	20.5654	1.59619
$167$	1.52626	0.118105	0.0590526	−	0.998255i	$-0.481192\pi$
$167$	1.52626	0.118105	0.0590526	+	0.998255i	$0.481192\pi$
$168$	88.5803	6.83412
$169$	−12.9719	−0.997835
$170$	−2.53605	−0.194506
$171$	−32.6101	−2.49376
$172$	5.13539	0.391570
$173$	−10.9673	−0.833825	−0.416913	−	0.908947i	$-0.636888\pi$
$173$	−10.9673	−0.833825	−0.416913	+	0.908947i	$0.636888\pi$
$174$	−61.9666	−4.69768
$175$	16.5406	1.25035
$176$	−12.1015	−0.912184
$177$	−23.7898	−1.78815
$178$	−9.03386	−0.677117
$179$	−16.9601	−1.26766	−0.633828	−	0.773474i	$-0.718517\pi$
$179$	−16.9601	−1.26766	−0.633828	+	0.773474i	$0.718517\pi$
$180$	18.8599	1.40573
$181$	8.65716	0.643482	0.321741	−	0.946828i	$-0.395732\pi$
$181$	8.65716	0.643482	0.321741	+	0.946828i	$0.395732\pi$
$182$	1.80864	0.134065
$183$	16.0739	1.18821
$184$	−43.7874	−3.22805
$185$	5.37633	0.395276
$186$	−41.6300	−3.05246
$187$	−1.00000	−0.0731272
$188$	12.3759	0.902604
$189$	−9.18309	−0.667972
$190$	21.3793	1.55102
$191$	−18.3254	−1.32598	−0.662989	−	0.748629i	$-0.730712\pi$
$191$	−18.3254	−1.32598	−0.662989	+	0.748629i	$0.730712\pi$
$192$	45.6044	3.29121
$193$	2.71391	0.195352	0.0976759	−	0.995218i	$-0.468859\pi$
$193$	2.71391	0.195352	0.0976759	+	0.995218i	$0.468859\pi$
$194$	16.7380	1.20172
$195$	0.417448	0.0298941
$196$	47.6892	3.40637
$197$	−20.0277	−1.42692	−0.713458	−	0.700698i	$-0.752872\pi$
$197$	−20.0277	−1.42692	−0.713458	+	0.700698i	$0.752872\pi$
$198$	10.3330	0.734333
$199$	17.7250	1.25649	0.628244	−	0.778016i	$-0.283774\pi$
$199$	17.7250	1.25649	0.628244	+	0.778016i	$0.283774\pi$
$200$	34.3274	2.42731
$201$	−11.1204	−0.784371
$202$	−36.0715	−2.53798
$203$	−35.7221	−2.50720
$204$	13.4585	0.942285
$205$	−1.62375	−0.113408
$206$	52.4527	3.65456
$207$	20.2239	1.40566
$208$	2.03034	0.140779
$209$	8.43016	0.583126
$210$	26.8222	1.85091
$211$	−6.59004	−0.453677	−0.226838	−	0.973932i	$-0.572839\pi$
$211$	−6.59004	−0.453677	−0.226838	+	0.973932i	$0.572839\pi$
$212$	−40.2407	−2.76374
$213$	−30.3436	−2.07911
$214$	−40.0860	−2.74022
$215$	0.949400	0.0647485
$216$	−19.0580	−1.29673
$217$	−23.9986	−1.62913
$218$	48.7787	3.30371
$219$	13.0905	0.884574
$220$	−4.87554	−0.328709
$221$	0.167776	0.0112858
$222$	−39.6432	−2.66068
$223$	2.99779	0.200747	0.100373	−	0.994950i	$-0.467996\pi$
$223$	2.99779	0.200747	0.100373	+	0.994950i	$0.467996\pi$
$224$	62.8553	4.19970
$225$	−15.8546	−1.05698
$226$	2.22125	0.147756
$227$	−15.8023	−1.04883	−0.524416	−	0.851462i	$-0.675716\pi$
$227$	−15.8023	−1.04883	−0.524416	+	0.851462i	$0.675716\pi$
$228$	−113.457	−7.51391
$229$	−22.5758	−1.49185	−0.745926	−	0.666028i	$-0.767993\pi$
$229$	−22.5758	−1.49185	−0.745926	+	0.666028i	$0.767993\pi$
$230$	−13.2588	−0.874262
$231$	10.5764	0.695873
$232$	−74.1355	−4.86723
$233$	−18.4714	−1.21010	−0.605051	−	0.796186i	$-0.706847\pi$
$233$	−18.4714	−1.21010	−0.605051	+	0.796186i	$0.706847\pi$
$234$	−1.73363	−0.113331
$235$	2.28798	0.149251
$236$	−46.6166	−3.03448
$237$	10.5803	0.687261
$238$	10.7801	0.698768
$239$	−8.75515	−0.566323	−0.283162	−	0.959072i	$-0.591383\pi$
$239$	−8.75515	−0.566323	−0.283162	+	0.959072i	$0.591383\pi$
$240$	30.1101	1.94360
$241$	7.41689	0.477764	0.238882	−	0.971049i	$-0.423219\pi$
$241$	7.41689	0.477764	0.238882	+	0.971049i	$0.423219\pi$
$242$	−2.67122	−0.171712
$243$	−21.6109	−1.38634
$244$	31.4971	2.01639
$245$	8.81649	0.563265
$246$	11.9730	0.763369
$247$	−1.41438	−0.0899948
$248$	−49.8052	−3.16263
$249$	−20.1768	−1.27865
$250$	23.0746	1.45937
$251$	−7.83995	−0.494853	−0.247427	−	0.968907i	$-0.579585\pi$
$251$	−7.83995	−0.494853	−0.247427	+	0.968907i	$0.579585\pi$
$252$	−80.1683	−5.05013
$253$	−5.22814	−0.328691
$254$	−26.7886	−1.68086
$255$	2.48813	0.155813
$256$	6.15416	0.384635
$257$	−1.22987	−0.0767174	−0.0383587	−	0.999264i	$-0.512213\pi$
$257$	−1.22987	−0.0767174	−0.0383587	+	0.999264i	$0.512213\pi$
$258$	−7.00056	−0.435836
$259$	−22.8533	−1.42004
$260$	0.818000	0.0507302
$261$	34.2406	2.11944
$262$	48.6710	3.00690
$263$	8.64291	0.532945	0.266472	−	0.963843i	$-0.414142\pi$
$263$	8.64291	0.532945	0.266472	+	0.963843i	$0.414142\pi$
$264$	21.9495	1.35090
$265$	−7.43946	−0.457002
$266$	−90.8777	−5.57207
$267$	8.86315	0.542416
$268$	−21.7906	−1.33108
$269$	−19.0649	−1.16241	−0.581203	−	0.813759i	$-0.697418\pi$
$269$	−19.0649	−1.16241	−0.581203	+	0.813759i	$0.697418\pi$
$270$	−5.77079	−0.351199
$271$	1.05569	0.0641285	0.0320643	−	0.999486i	$-0.489792\pi$
$271$	1.05569	0.0641285	0.0320643	+	0.999486i	$0.489792\pi$
$272$	12.1015	0.733760
$273$	−1.77446	−0.107395
$274$	2.14763	0.129743
$275$	4.09864	0.247157
$276$	70.3631	4.23536
$277$	−7.96483	−0.478560	−0.239280	−	0.970951i	$-0.576911\pi$
$277$	−7.96483	−0.478560	−0.239280	+	0.970951i	$0.576911\pi$
$278$	50.2881	3.01608
$279$	23.0033	1.37717
$280$	32.0895	1.91771
$281$	−4.96841	−0.296391	−0.148195	−	0.988958i	$-0.547346\pi$
$281$	−4.96841	−0.296391	−0.148195	+	0.988958i	$0.547346\pi$
$282$	−16.8708	−1.00464
$283$	−20.8777	−1.24105	−0.620526	−	0.784186i	$-0.713081\pi$
$283$	−20.8777	−1.24105	−0.620526	+	0.784186i	$0.713081\pi$
$284$	−59.4589	−3.52824
$285$	−20.9753	−1.24247
$286$	0.448166	0.0265006
$287$	6.90211	0.407419
$288$	−60.2485	−3.55017
$289$	1.00000	0.0588235
$290$	−22.4483	−1.31821
$291$	−16.4217	−0.962655
$292$	25.6511	1.50112
$293$	−6.95187	−0.406133	−0.203066	−	0.979165i	$-0.565091\pi$
$293$	−6.95187	−0.406133	−0.203066	+	0.979165i	$0.565091\pi$
$294$	−65.0099	−3.79145
$295$	−8.61819	−0.501770
$296$	−47.4283	−2.75672
$297$	−2.27550	−0.132038
$298$	−58.4993	−3.38877
$299$	0.877158	0.0507273
$300$	−55.1616	−3.18476
$301$	−4.03564	−0.232610
$302$	25.7923	1.48418
$303$	35.3898	2.03309
$304$	−102.017	−5.85110
$305$	5.82298	0.333423
$306$	−10.3330	−0.590697
$307$	22.5669	1.28796	0.643981	−	0.765041i	$-0.277282\pi$
$307$	22.5669	1.28796	0.643981	+	0.765041i	$0.277282\pi$
$308$	20.7246	1.18089
$309$	−51.4615	−2.92755
$310$	−15.0810	−0.856546
$311$	−14.5578	−0.825500	−0.412750	−	0.910844i	$-0.635432\pi$
$311$	−14.5578	−0.825500	−0.412750	+	0.910844i	$0.635432\pi$
$312$	−3.68260	−0.208486
$313$	−3.55013	−0.200665	−0.100333	−	0.994954i	$-0.531991\pi$
$313$	−3.55013	−0.200665	−0.100333	+	0.994954i	$0.531991\pi$
$314$	−42.8523	−2.41830
$315$	−14.8210	−0.835070
$316$	20.7322	1.16628
$317$	−30.2570	−1.69940	−0.849702	−	0.527263i	$-0.823218\pi$
$317$	−30.2570	−1.69940	−0.849702	+	0.527263i	$0.823218\pi$
$318$	54.8561	3.07617
$319$	−8.85167	−0.495598
$320$	16.5208	0.923543
$321$	39.3285	2.19510
$322$	56.3597	3.14080
$323$	−8.43016	−0.469067
$324$	−28.9704	−1.60946
$325$	−0.687654	−0.0381442
$326$	−41.7187	−2.31058
$327$	−47.8570	−2.64650
$328$	14.3242	0.790923
$329$	−9.72556	−0.536188
$330$	6.64633	0.365868
$331$	−16.7959	−0.923184	−0.461592	−	0.887092i	$-0.652722\pi$
$331$	−16.7959	−0.923184	−0.461592	+	0.887092i	$0.652722\pi$
$332$	−39.5369	−2.16987
$333$	21.9055	1.20041
$334$	−4.07696	−0.223081
$335$	−4.02852	−0.220101
$336$	−127.990	−6.98240
$337$	8.22214	0.447888	0.223944	−	0.974602i	$-0.428107\pi$
$337$	8.22214	0.447888	0.223944	+	0.974602i	$0.428107\pi$
$338$	34.6506	1.88474
$339$	−2.17928	−0.118362
$340$	4.87554	0.264413
$341$	−5.94666	−0.322030
$342$	87.1086	4.71029
$343$	−9.22703	−0.498213
$344$	−8.37532	−0.451567
$345$	13.0083	0.700343
$346$	29.2959	1.57496
$347$	8.49821	0.456208	0.228104	−	0.973637i	$-0.426747\pi$
$347$	8.49821	0.456208	0.228104	+	0.973637i	$0.426747\pi$
$348$	119.130	6.38606
$349$	27.7391	1.48484	0.742420	−	0.669934i	$-0.233678\pi$
$349$	27.7391	1.48484	0.742420	+	0.669934i	$0.233678\pi$
$350$	−44.1836	−2.36171
$351$	0.381774	0.0203776
$352$	15.5751	0.830153
$353$	−7.63207	−0.406214	−0.203107	−	0.979157i	$-0.565104\pi$
$353$	−7.63207	−0.406214	−0.203107	+	0.979157i	$0.565104\pi$
$354$	63.5476	3.37752
$355$	−10.9924	−0.583416
$356$	17.3675	0.920478
$357$	−10.5764	−0.559760
$358$	45.3040	2.39439
$359$	−34.4022	−1.81568	−0.907839	−	0.419318i	$-0.862269\pi$
$359$	−34.4022	−1.81568	−0.907839	+	0.419318i	$0.862269\pi$
$360$	−30.7586	−1.62112
$361$	52.0676	2.74040
$362$	−23.1251	−1.21543
$363$	2.62074	0.137553
$364$	−3.47709	−0.182249
$365$	4.74222	0.248219
$366$	−42.9367	−2.24434
$367$	25.6282	1.33778	0.668891	−	0.743360i	$-0.266769\pi$
$367$	25.6282	1.33778	0.668891	+	0.743360i	$0.266769\pi$
$368$	63.2683	3.29809
$369$	−6.61586	−0.344408
$370$	−14.3613	−0.746610
$371$	31.6231	1.64179
$372$	80.0333	4.14953
$373$	−35.5160	−1.83895	−0.919476	−	0.393147i	$-0.871386\pi$
$373$	−35.5160	−1.83895	−0.919476	+	0.393147i	$0.871386\pi$
$374$	2.67122	0.138125
$375$	−22.6386	−1.16905
$376$	−20.1838	−1.04090
$377$	1.48510	0.0764865
$378$	24.5300	1.26169
$379$	−0.741015	−0.0380634	−0.0190317	−	0.999819i	$-0.506058\pi$
$379$	−0.741015	−0.0380634	−0.0190317	+	0.999819i	$0.506058\pi$
$380$	−41.1016	−2.10847
$381$	26.2823	1.34648
$382$	48.9511	2.50455
$383$	−1.63497	−0.0835432	−0.0417716	−	0.999127i	$-0.513300\pi$
$383$	−1.63497	−0.0835432	−0.0417716	+	0.999127i	$0.513300\pi$
$384$	−40.1829	−2.05058
$385$	3.83144	0.195268
$386$	−7.24945	−0.368987
$387$	3.86827	0.196635
$388$	−32.1786	−1.63362
$389$	−17.2922	−0.876747	−0.438373	−	0.898793i	$-0.644445\pi$
$389$	−17.2922	−0.876747	−0.438373	+	0.898793i	$0.644445\pi$
$390$	−1.11510	−0.0564650
$391$	5.22814	0.264399
$392$	−77.7764	−3.92830
$393$	−47.7513	−2.40873
$394$	53.4984	2.69521
$395$	3.83285	0.192852
$396$	−19.8651	−0.998258
$397$	−6.13451	−0.307882	−0.153941	−	0.988080i	$-0.549197\pi$
$397$	−6.13451	−0.307882	−0.153941	+	0.988080i	$0.549197\pi$
$398$	−47.3472	−2.37330
$399$	89.1603	4.46360
$400$	−49.5996	−2.47998
$401$	−4.41238	−0.220344	−0.110172	−	0.993913i	$-0.535140\pi$
$401$	−4.41238	−0.220344	−0.110172	+	0.993913i	$0.535140\pi$
$402$	29.7049	1.48155
$403$	0.997708	0.0496994
$404$	69.3472	3.45015
$405$	−5.35586	−0.266135
$406$	95.4216	4.73569
$407$	−5.66287	−0.280698
$408$	−21.9495	−1.08666
$409$	3.56821	0.176437	0.0882184	−	0.996101i	$-0.471883\pi$
$409$	3.56821	0.176437	0.0882184	+	0.996101i	$0.471883\pi$
$410$	4.33738	0.214208
$411$	−2.10704	−0.103933
$412$	−100.840	−4.96803
$413$	36.6336	1.80262
$414$	−54.0223	−2.65505
$415$	−7.30934	−0.358801
$416$	−2.61312	−0.128119
$417$	−49.3378	−2.41608
$418$	−22.5188	−1.10143
$419$	−19.3093	−0.943320	−0.471660	−	0.881780i	$-0.656345\pi$
$419$	−19.3093	−0.943320	−0.471660	+	0.881780i	$0.656345\pi$
$420$	−51.5655	−2.51614
$421$	21.6769	1.05647	0.528234	−	0.849099i	$-0.322854\pi$
$421$	21.6769	1.05647	0.528234	+	0.849099i	$0.322854\pi$
$422$	17.6034	0.856921
$423$	9.32221	0.453261
$424$	65.6286	3.18721
$425$	−4.09864	−0.198813
$426$	81.0543	3.92709
$427$	−24.7519	−1.19783
$428$	77.0651	3.72508
$429$	−0.439697	−0.0212288
$430$	−2.53605	−0.122299
$431$	34.1955	1.64714	0.823570	−	0.567215i	$-0.191979\pi$
$431$	34.1955	1.64714	0.823570	+	0.567215i	$0.191979\pi$
$432$	27.5369	1.32487
$433$	25.9097	1.24514	0.622570	−	0.782564i	$-0.286089\pi$
$433$	25.9097	1.24514	0.622570	+	0.782564i	$0.286089\pi$
$434$	64.1054	3.07716
$435$	22.0241	1.05597
$436$	−93.7768	−4.49109
$437$	−44.0741	−2.10835
$438$	−34.9676	−1.67081
$439$	−29.3524	−1.40091	−0.700456	−	0.713695i	$-0.747020\pi$
$439$	−29.3524	−1.40091	−0.700456	+	0.713695i	$0.747020\pi$
$440$	7.95152	0.379074
$441$	35.9222	1.71058
$442$	−0.448166	−0.0213171
$443$	−19.2972	−0.916838	−0.458419	−	0.888736i	$-0.651584\pi$
$443$	−19.2972	−0.916838	−0.458419	+	0.888736i	$0.651584\pi$
$444$	76.2139	3.61695
$445$	3.21080	0.152207
$446$	−8.00774	−0.379177
$447$	57.3938	2.71463
$448$	−70.2256	−3.31785
$449$	0.450571	0.0212637	0.0106319	−	0.999943i	$-0.496616\pi$
$449$	0.450571	0.0212637	0.0106319	+	0.999943i	$0.496616\pi$
$450$	42.3511	1.99645
$451$	1.71029	0.0805344
$452$	−4.27035	−0.200860
$453$	−25.3049	−1.18893
$454$	42.2112	1.98107
$455$	−0.642823	−0.0301360
$456$	185.038	8.66519
$457$	6.88978	0.322290	0.161145	−	0.986931i	$-0.448481\pi$
$457$	6.88978	0.322290	0.161145	+	0.986931i	$0.448481\pi$
$458$	60.3049	2.81786
$459$	2.27550	0.106211
$460$	25.4900	1.18848
$461$	−4.39969	−0.204914	−0.102457	−	0.994737i	$-0.532670\pi$
$461$	−4.39969	−0.204914	−0.102457	+	0.994737i	$0.532670\pi$
$462$	−28.2517	−1.31439
$463$	8.95224	0.416046	0.208023	−	0.978124i	$-0.433297\pi$
$463$	8.95224	0.416046	0.208023	+	0.978124i	$0.433297\pi$
$464$	107.118	4.97284
$465$	14.7961	0.686151
$466$	49.3411	2.28568
$467$	42.2207	1.95374	0.976870	−	0.213835i	$-0.0685954\pi$
$467$	42.2207	1.95374	0.976870	+	0.213835i	$0.0685954\pi$
$468$	3.33288	0.154063
$469$	17.1241	0.790719
$470$	−6.11168	−0.281911
$471$	42.0425	1.93722
$472$	76.0270	3.49943
$473$	−1.00000	−0.0459800
$474$	−28.2621	−1.29812
$475$	34.5522	1.58536
$476$	−20.7246	−0.949910
$477$	−30.3116	−1.38787
$478$	23.3869	1.06969
$479$	−25.7835	−1.17808	−0.589038	−	0.808105i	$-0.700493\pi$
$479$	−25.7835	−1.17808	−0.589038	+	0.808105i	$0.700493\pi$
$480$	−38.7527	−1.76881
$481$	0.950094	0.0433206
$482$	−19.8121	−0.902418
$483$	−55.2947	−2.51600
$484$	5.13539	0.233427
$485$	−5.94898	−0.270129
$486$	57.7274	2.61857
$487$	−23.0585	−1.04488	−0.522439	−	0.852676i	$-0.674978\pi$
$487$	−23.0585	−1.04488	−0.522439	+	0.852676i	$0.674978\pi$
$488$	−51.3686	−2.32535
$489$	40.9303	1.85093
$490$	−23.5508	−1.06391
$491$	0.592782	0.0267519	0.0133759	−	0.999911i	$-0.495742\pi$
$491$	0.592782	0.0267519	0.0133759	+	0.999911i	$0.495742\pi$
$492$	−23.0180	−1.03773
$493$	8.85167	0.398659
$494$	3.77811	0.169985
$495$	−3.67253	−0.165068
$496$	71.9635	3.23126
$497$	46.7257	2.09593
$498$	53.8966	2.41516
$499$	−15.1449	−0.677980	−0.338990	−	0.940790i	$-0.610085\pi$
$499$	−15.1449	−0.677980	−0.338990	+	0.940790i	$0.610085\pi$
$500$	−44.3608	−1.98388
$501$	3.99991	0.178703
$502$	20.9422	0.934697
$503$	−14.0043	−0.624419	−0.312210	−	0.950013i	$-0.601069\pi$
$503$	−14.0043	−0.624419	−0.312210	+	0.950013i	$0.601069\pi$
$504$	130.746	5.82391
$505$	12.8205	0.570504
$506$	13.9655	0.620842
$507$	−33.9958	−1.50981
$508$	51.5008	2.28498
$509$	7.75138	0.343574	0.171787	−	0.985134i	$-0.445046\pi$
$509$	7.75138	0.343574	0.171787	+	0.985134i	$0.445046\pi$
$510$	−6.64633	−0.294304
$511$	−20.1579	−0.891733
$512$	14.2262	0.628717
$513$	−19.1828	−0.846942
$514$	3.28526	0.144907
$515$	−18.6427	−0.821495
$516$	13.4585	0.592478
$517$	−2.40992	−0.105988
$518$	61.0461	2.68221
$519$	−28.7423	−1.26165
$520$	−1.33408	−0.0585031
$521$	4.15859	0.182191	0.0910956	−	0.995842i	$-0.470963\pi$
$521$	4.15859	0.182191	0.0910956	+	0.995842i	$0.470963\pi$
$522$	−91.4641	−4.00327
$523$	−29.0024	−1.26819	−0.634094	−	0.773256i	$-0.718627\pi$
$523$	−29.0024	−1.26819	−0.634094	+	0.773256i	$0.718627\pi$
$524$	−93.5697	−4.08761
$525$	43.3487	1.89189
$526$	−23.0871	−1.00664
$527$	5.94666	0.259041
$528$	−31.7148	−1.38021
$529$	4.33349	0.188412
$530$	19.8724	0.863202
$531$	−35.1142	−1.52383
$532$	174.712	7.57471
$533$	−0.286946	−0.0124290
$534$	−23.6754	−1.02453
$535$	14.2473	0.615965
$536$	35.5384	1.53502
$537$	−44.4479	−1.91807
$538$	50.9264	2.19559
$539$	−9.28639	−0.399993
$540$	11.0943	0.477422
$541$	−7.47108	−0.321207	−0.160604	−	0.987019i	$-0.551344\pi$
$541$	−7.47108	−0.321207	−0.160604	+	0.987019i	$0.551344\pi$
$542$	−2.81997	−0.121128
$543$	22.6882	0.973642
$544$	−15.5751	−0.667775
$545$	−17.3369	−0.742630
$546$	4.73996	0.202852
$547$	−15.6496	−0.669128	−0.334564	−	0.942373i	$-0.608589\pi$
$547$	−15.6496	−0.669128	−0.334564	+	0.942373i	$0.608589\pi$
$548$	−4.12880	−0.176374
$549$	23.7254	1.01257
$550$	−10.9484	−0.466839
$551$	−74.6210	−3.17896
$552$	−114.755	−4.88430
$553$	−16.2924	−0.692823
$554$	21.2758	0.903921
$555$	14.0899	0.598085
$556$	−96.6785	−4.10008
$557$	9.34255	0.395857	0.197928	−	0.980216i	$-0.436579\pi$
$557$	9.34255	0.395857	0.197928	+	0.980216i	$0.436579\pi$
$558$	−61.4467	−2.60125
$559$	0.167776	0.00709617
$560$	−46.3661	−1.95932
$561$	−2.62074	−0.110648
$562$	13.2717	0.559833
$563$	16.4963	0.695236	0.347618	−	0.937636i	$-0.386991\pi$
$563$	16.4963	0.695236	0.347618	+	0.937636i	$0.386991\pi$
$564$	32.4339	1.36572
$565$	−0.789475	−0.0332135
$566$	55.7689	2.34414
$567$	22.7663	0.956095
$568$	96.9716	4.06884
$569$	4.77889	0.200341	0.100171	−	0.994970i	$-0.468061\pi$
$569$	4.77889	0.200341	0.100171	+	0.994970i	$0.468061\pi$
$570$	56.0296	2.34682
$571$	36.5704	1.53043	0.765213	−	0.643778i	$-0.222634\pi$
$571$	36.5704	1.53043	0.765213	+	0.643778i	$0.222634\pi$
$572$	−0.861596	−0.0360252
$573$	−48.0260	−2.00632
$574$	−18.4370	−0.769547
$575$	−21.4283	−0.893621
$576$	67.3131	2.80471
$577$	−26.2557	−1.09304	−0.546519	−	0.837447i	$-0.684047\pi$
$577$	−26.2557	−1.09304	−0.546519	+	0.837447i	$0.684047\pi$
$578$	−2.67122	−0.111108
$579$	7.11245	0.295583
$580$	43.1567	1.79198
$581$	31.0700	1.28900
$582$	43.8658	1.81830
$583$	7.83596	0.324532
$584$	−41.8344	−1.73112
$585$	0.616163	0.0254752
$586$	18.5699	0.767117
$587$	10.1219	0.417776	0.208888	−	0.977940i	$-0.433016\pi$
$587$	10.1219	0.417776	0.208888	+	0.977940i	$0.433016\pi$
$588$	124.981	5.15413
$589$	−50.1313	−2.06563
$590$	23.0210	0.947761
$591$	−52.4874	−2.15904
$592$	68.5291	2.81653
$593$	13.2856	0.545575	0.272787	−	0.962074i	$-0.412054\pi$
$593$	13.2856	0.545575	0.272787	+	0.962074i	$0.412054\pi$
$594$	6.07835	0.249398
$595$	−3.83144	−0.157074
$596$	112.464	4.60672
$597$	46.4525	1.90117
$598$	−2.34308	−0.0958156
$599$	−35.6049	−1.45478	−0.727388	−	0.686227i	$-0.759266\pi$
$599$	−35.6049	−1.45478	−0.727388	+	0.686227i	$0.759266\pi$
$600$	89.9631	3.67273
$601$	−5.60169	−0.228498	−0.114249	−	0.993452i	$-0.536446\pi$
$601$	−5.60169	−0.228498	−0.114249	+	0.993452i	$0.536446\pi$
$602$	10.7801	0.439363
$603$	−16.4139	−0.668427
$604$	−49.5856	−2.01761
$605$	0.949400	0.0385986
$606$	−94.5339	−3.84018
$607$	−34.1744	−1.38710	−0.693548	−	0.720410i	$-0.743954\pi$
$607$	−34.1744	−1.38710	−0.693548	+	0.720410i	$0.743954\pi$
$608$	131.300	5.32492
$609$	−93.6184	−3.79361
$610$	−15.5544	−0.629781
$611$	0.404327	0.0163573
$612$	19.8651	0.802998
$613$	18.7263	0.756348	0.378174	−	0.925735i	$-0.376552\pi$
$613$	18.7263	0.756348	0.378174	+	0.925735i	$0.376552\pi$
$614$	−60.2811	−2.43275
$615$	−4.25542	−0.171595
$616$	−33.7998	−1.36183
$617$	−24.0661	−0.968865	−0.484433	−	0.874829i	$-0.660974\pi$
$617$	−24.0661	−0.968865	−0.484433	+	0.874829i	$0.660974\pi$
$618$	137.465	5.52965
$619$	5.08877	0.204535	0.102267	−	0.994757i	$-0.467390\pi$
$619$	5.08877	0.204535	0.102267	+	0.994757i	$0.467390\pi$
$620$	28.9932	1.16440
$621$	11.8966	0.477396
$622$	38.8872	1.55923
$623$	−13.6482	−0.546806
$624$	5.32099	0.213010
$625$	12.2920	0.491682
$626$	9.48317	0.379024
$627$	22.0932	0.882319
$628$	82.3833	3.28745
$629$	5.66287	0.225793
$630$	39.5901	1.57731
$631$	29.8693	1.18908	0.594539	−	0.804067i	$-0.297335\pi$
$631$	29.8693	1.18908	0.594539	+	0.804067i	$0.297335\pi$
$632$	−33.8122	−1.34498
$633$	−17.2708	−0.686451
$634$	80.8231	3.20989
$635$	9.52115	0.377835
$636$	−105.460	−4.18178
$637$	1.55803	0.0617315
$638$	23.6447	0.936103
$639$	−44.7878	−1.77178
$640$	−14.5568	−0.575410
$641$	−39.0237	−1.54134	−0.770672	−	0.637232i	$-0.780079\pi$
$641$	−39.0237	−1.54134	−0.770672	+	0.637232i	$0.780079\pi$
$642$	−105.055	−4.14619
$643$	−9.14378	−0.360595	−0.180298	−	0.983612i	$-0.557706\pi$
$643$	−9.14378	−0.360595	−0.180298	+	0.983612i	$0.557706\pi$
$644$	−108.351	−4.26963
$645$	2.48813	0.0979700
$646$	22.5188	0.885989
$647$	−4.33675	−0.170495	−0.0852477	−	0.996360i	$-0.527168\pi$
$647$	−4.33675	−0.170495	−0.0852477	+	0.996360i	$0.527168\pi$
$648$	47.2478	1.85607
$649$	9.07751	0.356323
$650$	1.83687	0.0720480
$651$	−62.8940	−2.46501
$652$	80.2039	3.14103
$653$	6.98784	0.273455	0.136728	−	0.990609i	$-0.456342\pi$
$653$	6.98784	0.273455	0.136728	+	0.990609i	$0.456342\pi$
$654$	127.836	4.99879
$655$	−17.2986	−0.675912
$656$	−20.6970	−0.808084
$657$	19.3219	0.753818
$658$	25.9791	1.01277
$659$	32.3388	1.25974	0.629871	−	0.776700i	$-0.283108\pi$
$659$	32.3388	1.25974	0.629871	+	0.776700i	$0.283108\pi$
$660$	−12.7775	−0.497364
$661$	−37.6419	−1.46410	−0.732050	−	0.681251i	$-0.761436\pi$
$661$	−37.6419	−1.46410	−0.732050	+	0.681251i	$0.761436\pi$
$662$	44.8654	1.74374
$663$	0.439697	0.0170764
$664$	64.4807	2.50234
$665$	32.2996	1.25253
$666$	−58.5143	−2.26738
$667$	46.2778	1.79188
$668$	7.83792	0.303258
$669$	7.85642	0.303747
$670$	10.7610	0.415735
$671$	−6.13333	−0.236775
$672$	164.727	6.35449
$673$	28.4658	1.09728	0.548639	−	0.836060i	$-0.315146\pi$
$673$	28.4658	1.09728	0.548639	+	0.836060i	$0.315146\pi$
$674$	−21.9631	−0.845987
$675$	−9.32645	−0.358975
$676$	−66.6156	−2.56214
$677$	9.69865	0.372749	0.186375	−	0.982479i	$-0.440326\pi$
$677$	9.69865	0.372749	0.186375	+	0.982479i	$0.440326\pi$
$678$	5.82133	0.223567
$679$	25.2875	0.970445
$680$	−7.95152	−0.304927
$681$	−41.4136	−1.58697
$682$	15.8848	0.608261
$683$	9.07541	0.347261	0.173630	−	0.984811i	$-0.444450\pi$
$683$	9.07541	0.347261	0.173630	+	0.984811i	$0.444450\pi$
$684$	−167.466	−6.40321
$685$	−0.763307	−0.0291645
$686$	24.6474	0.941041
$687$	−59.1653	−2.25730
$688$	12.1015	0.461365
$689$	−1.31469	−0.0500856
$690$	−34.7480	−1.32283
$691$	41.2002	1.56733	0.783665	−	0.621184i	$-0.213348\pi$
$691$	41.2002	1.56733	0.783665	+	0.621184i	$0.213348\pi$
$692$	−56.3212	−2.14101
$693$	15.6109	0.593010
$694$	−22.7005	−0.861701
$695$	−17.8733	−0.677974
$696$	−194.290	−7.36453
$697$	−1.71029	−0.0647818
$698$	−74.0972	−2.80462
$699$	−48.4087	−1.83099
$700$	84.9427	3.21053
$701$	10.0973	0.381368	0.190684	−	0.981651i	$-0.438929\pi$
$701$	10.0973	0.381368	0.190684	+	0.981651i	$0.438929\pi$
$702$	−1.01980	−0.0384899
$703$	−47.7389	−1.80051
$704$	−17.4014	−0.655838
$705$	5.99619	0.225829
$706$	20.3869	0.767271
$707$	−54.4963	−2.04955
$708$	−122.170	−4.59142
$709$	11.6574	0.437804	0.218902	−	0.975747i	$-0.429752\pi$
$709$	11.6574	0.437804	0.218902	+	0.975747i	$0.429752\pi$
$710$	29.3631	1.10198
$711$	15.6167	0.585671
$712$	−28.3247	−1.06151
$713$	31.0900	1.16433
$714$	28.2517	1.05729
$715$	−0.159287	−0.00595698
$716$	−87.0967	−3.25496
$717$	−22.9449	−0.856895
$718$	91.8957	3.42952
$719$	−36.3273	−1.35478	−0.677390	−	0.735624i	$-0.736889\pi$
$719$	−36.3273	−1.35478	−0.677390	+	0.735624i	$0.736889\pi$
$720$	44.4431	1.65630
$721$	79.2450	2.95124
$722$	−139.084	−5.17616
$723$	19.4377	0.722897
$724$	44.4579	1.65227
$725$	−36.2798	−1.34740
$726$	−7.00056	−0.259815
$727$	−15.6139	−0.579087	−0.289543	−	0.957165i	$-0.593503\pi$
$727$	−15.6139	−0.579087	−0.289543	+	0.957165i	$0.593503\pi$
$728$	5.67079	0.210173
$729$	−39.7126	−1.47084
$730$	−12.6675	−0.468845
$731$	1.00000	0.0369863
$732$	82.5456	3.05097
$733$	−3.11550	−0.115073	−0.0575367	−	0.998343i	$-0.518325\pi$
$733$	−3.11550	−0.115073	−0.0575367	+	0.998343i	$0.518325\pi$
$734$	−68.4585	−2.52685
$735$	23.1057	0.852267
$736$	−81.4286	−3.00150
$737$	4.24323	0.156301
$738$	17.6724	0.650529
$739$	51.5071	1.89472	0.947359	−	0.320174i	$-0.103741\pi$
$739$	51.5071	1.89472	0.947359	+	0.320174i	$0.103741\pi$
$740$	27.6096	1.01495
$741$	−3.70672	−0.136170
$742$	−84.4721	−3.10107
$743$	50.6592	1.85851	0.929253	−	0.369444i	$-0.120452\pi$
$743$	50.6592	1.85851	0.929253	+	0.369444i	$0.120452\pi$
$744$	−130.526	−4.78533
$745$	20.7917	0.761750
$746$	94.8710	3.47348
$747$	−29.7814	−1.08964
$748$	−5.13539	−0.187769
$749$	−60.5615	−2.21287
$750$	60.4725	2.20815
$751$	−22.8286	−0.833029	−0.416514	−	0.909129i	$-0.636748\pi$
$751$	−22.8286	−0.833029	−0.416514	+	0.909129i	$0.636748\pi$
$752$	29.1636	1.06349
$753$	−20.5465	−0.748755
$754$	−3.96702	−0.144470
$755$	−9.16708	−0.333624
$756$	−47.1588	−1.71515
$757$	41.9916	1.52621	0.763105	−	0.646275i	$-0.223674\pi$
$757$	41.9916	1.52621	0.763105	+	0.646275i	$0.223674\pi$
$758$	1.97941	0.0718954
$759$	−13.7016	−0.497336
$760$	67.0326	2.43153
$761$	46.4945	1.68542	0.842711	−	0.538366i	$-0.180958\pi$
$761$	46.4945	1.68542	0.842711	+	0.538366i	$0.180958\pi$
$762$	−70.2058	−2.54329
$763$	73.6943	2.66791
$764$	−94.1081	−3.40471
$765$	3.67253	0.132781
$766$	4.36736	0.157799
$767$	−1.52299	−0.0549920
$768$	16.1285	0.581985
$769$	9.22702	0.332735	0.166367	−	0.986064i	$-0.446796\pi$
$769$	9.22702	0.332735	0.166367	+	0.986064i	$0.446796\pi$
$770$	−10.2346	−0.368829
$771$	−3.22318	−0.116080
$772$	13.9370	0.501604
$773$	24.3518	0.875875	0.437937	−	0.899005i	$-0.355709\pi$
$773$	24.3518	0.875875	0.437937	+	0.899005i	$0.355709\pi$
$774$	−10.3330	−0.371411
$775$	−24.3732	−0.875512
$776$	52.4801	1.88393
$777$	−59.8925	−2.14863
$778$	46.1911	1.65603
$779$	14.4180	0.516579
$780$	2.14376	0.0767590
$781$	11.5783	0.414303
$782$	−13.9655	−0.499405
$783$	20.1420	0.719815
$784$	112.379	4.01354
$785$	15.2305	0.543600
$786$	127.554	4.54970
$787$	−26.1069	−0.930609	−0.465304	−	0.885151i	$-0.654055\pi$
$787$	−26.1069	−0.930609	−0.465304	+	0.885151i	$0.654055\pi$
$788$	−102.850	−3.66389
$789$	22.6508	0.806390
$790$	−10.2384	−0.364265
$791$	3.35584	0.119320
$792$	32.3980	1.15121
$793$	1.02903	0.0365418
$794$	16.3866	0.581539
$795$	−19.4969	−0.691483
$796$	91.0246	3.22628
$797$	54.5131	1.93095	0.965476	−	0.260493i	$-0.0838850\pi$
$797$	54.5131	1.93095	0.965476	+	0.260493i	$0.0838850\pi$
$798$	−238.167	−8.43100
$799$	2.40992	0.0852568
$800$	63.8365	2.25696
$801$	13.0822	0.462237
$802$	11.7864	0.416193
$803$	−4.99497	−0.176269
$804$	−57.1076	−2.01403
$805$	−20.0313	−0.706010
$806$	−2.66509	−0.0938739
$807$	−49.9640	−1.75882
$808$	−113.098	−3.97878
$809$	−33.3485	−1.17247	−0.586235	−	0.810141i	$-0.699390\pi$
$809$	−33.3485	−1.17247	−0.586235	+	0.810141i	$0.699390\pi$
$810$	14.3067	0.502685
$811$	−22.8260	−0.801530	−0.400765	−	0.916181i	$-0.631256\pi$
$811$	−22.8260	−0.801530	−0.400765	+	0.916181i	$0.631256\pi$
$812$	−183.447	−6.43774
$813$	2.76668	0.0970318
$814$	15.1267	0.530192
$815$	14.8276	0.519388
$816$	31.7148	1.11024
$817$	−8.43016	−0.294934
$818$	−9.53146	−0.333260
$819$	−2.61914	−0.0915202
$820$	−8.33859	−0.291196
$821$	−48.9846	−1.70958	−0.854788	−	0.518978i	$-0.826313\pi$
$821$	−48.9846	−1.70958	−0.854788	+	0.518978i	$0.826313\pi$
$822$	5.62837	0.196312
$823$	45.9147	1.60049	0.800243	−	0.599676i	$-0.204704\pi$
$823$	45.9147	1.60049	0.800243	+	0.599676i	$0.204704\pi$
$824$	164.460	5.72924
$825$	10.7415	0.373970
$826$	−97.8561	−3.40485
$827$	−7.96108	−0.276834	−0.138417	−	0.990374i	$-0.544201\pi$
$827$	−7.96108	−0.276834	−0.138417	+	0.990374i	$0.544201\pi$
$828$	103.857	3.60930
$829$	10.8082	0.375386	0.187693	−	0.982228i	$-0.439899\pi$
$829$	10.8082	0.375386	0.187693	+	0.982228i	$0.439899\pi$
$830$	19.5248	0.677716
$831$	−20.8737	−0.724101
$832$	2.91953	0.101217
$833$	9.28639	0.321754
$834$	131.792	4.56358
$835$	1.44903	0.0501456
$836$	43.2922	1.49729
$837$	13.5316	0.467722
$838$	51.5793	1.78178
$839$	10.8435	0.374357	0.187179	−	0.982326i	$-0.440066\pi$
$839$	10.8435	0.374357	0.187179	+	0.982326i	$0.440066\pi$
$840$	84.0981	2.90166
$841$	49.3520	1.70179
$842$	−57.9037	−1.99549
$843$	−13.0209	−0.448464
$844$	−33.8424	−1.16490
$845$	−12.3155	−0.423665
$846$	−24.9016	−0.856136
$847$	−4.03564	−0.138666
$848$	−94.8267	−3.25636
$849$	−54.7151	−1.87782
$850$	10.9484	0.375525
$851$	29.6063	1.01489
$852$	−155.826	−5.33852
$853$	29.0348	0.994132	0.497066	−	0.867713i	$-0.334411\pi$
$853$	29.0348	0.994132	0.497066	+	0.867713i	$0.334411\pi$
$854$	66.1177	2.26250
$855$	−30.9600	−1.05881
$856$	−125.685	−4.29584
$857$	−22.9067	−0.782479	−0.391240	−	0.920289i	$-0.627954\pi$
$857$	−22.9067	−0.782479	−0.391240	+	0.920289i	$0.627954\pi$
$858$	1.17453	0.0400977
$859$	50.8516	1.73503	0.867517	−	0.497408i	$-0.165715\pi$
$859$	50.8516	1.73503	0.867517	+	0.497408i	$0.165715\pi$
$860$	4.87554	0.166255
$861$	18.0886	0.616459
$862$	−91.3436	−3.11117
$863$	53.3484	1.81600	0.908000	−	0.418969i	$-0.137609\pi$
$863$	53.3484	1.81600	0.908000	+	0.418969i	$0.137609\pi$
$864$	−35.4410	−1.20573
$865$	−10.4123	−0.354029
$866$	−69.2103	−2.35186
$867$	2.62074	0.0890049
$868$	−123.242	−4.18311
$869$	−4.03713	−0.136950
$870$	−58.8311	−1.99456
$871$	−0.711912	−0.0241222
$872$	152.941	5.17922
$873$	−24.2387	−0.820357
$874$	117.731	3.98232
$875$	34.8609	1.17851
$876$	67.2249	2.27132
$877$	−3.72789	−0.125882	−0.0629409	−	0.998017i	$-0.520048\pi$
$877$	−3.72789	−0.125882	−0.0629409	+	0.998017i	$0.520048\pi$
$878$	78.4066	2.64609
$879$	−18.2190	−0.614513
$880$	−11.4892	−0.387299
$881$	−12.4484	−0.419399	−0.209699	−	0.977766i	$-0.567249\pi$
$881$	−12.4484	−0.419399	−0.209699	+	0.977766i	$0.567249\pi$
$882$	−95.9560	−3.23101
$883$	23.2800	0.783433	0.391716	−	0.920086i	$-0.371881\pi$
$883$	23.2800	0.783433	0.391716	+	0.920086i	$0.371881\pi$
$884$	0.861596	0.0289786
$885$	−22.5860	−0.759220
$886$	51.5470	1.73176
$887$	−18.0951	−0.607575	−0.303788	−	0.952740i	$-0.598251\pi$
$887$	−18.0951	−0.607575	−0.303788	+	0.952740i	$0.598251\pi$
$888$	−124.297	−4.17114
$889$	−40.4718	−1.35738
$890$	−8.57675	−0.287493
$891$	5.64131	0.188991
$892$	15.3948	0.515457
$893$	−20.3160	−0.679849
$894$	−153.311	−5.12749
$895$	−16.1019	−0.538227
$896$	61.8771	2.06717
$897$	2.29880	0.0767547
$898$	−1.20357	−0.0401637
$899$	52.6379	1.75557
$900$	−81.4198	−2.71399
$901$	−7.83596	−0.261054
$902$	−4.56855	−0.152116
$903$	−10.5764	−0.351959
$904$	6.96451	0.231636
$905$	8.21911	0.273212
$906$	67.5950	2.24569
$907$	32.6032	1.08257	0.541286	−	0.840839i	$-0.317938\pi$
$907$	32.6032	1.08257	0.541286	+	0.840839i	$0.317938\pi$
$908$	−81.1508	−2.69308
$909$	52.2362	1.73256
$910$	1.71712	0.0569220
$911$	−16.7868	−0.556171	−0.278086	−	0.960556i	$-0.589700\pi$
$911$	−16.7868	−0.556171	−0.278086	+	0.960556i	$0.589700\pi$
$912$	−267.361	−8.85321
$913$	7.69890	0.254796
$914$	−18.4041	−0.608753
$915$	15.2605	0.504497
$916$	−115.936	−3.83063
$917$	73.5315	2.42823
$918$	−6.07835	−0.200615
$919$	−18.7918	−0.619884	−0.309942	−	0.950755i	$-0.600310\pi$
$919$	−18.7918	−0.619884	−0.309942	+	0.950755i	$0.600310\pi$
$920$	−41.5717	−1.37058
$921$	59.1420	1.94879
$922$	11.7525	0.387049
$923$	−1.94256	−0.0639400
$924$	54.3137	1.78679
$925$	−23.2101	−0.763142
$926$	−23.9134	−0.785842
$927$	−75.9584	−2.49480
$928$	−137.865	−4.52565
$929$	3.05221	0.100140	0.0500698	−	0.998746i	$-0.484056\pi$
$929$	3.05221	0.100140	0.0500698	+	0.998746i	$0.484056\pi$
$930$	−39.5235	−1.29603
$931$	−78.2857	−2.56571
$932$	−94.8580	−3.10718
$933$	−38.1523	−1.24905
$934$	−112.781	−3.69029
$935$	−0.949400	−0.0310487
$936$	−5.43560	−0.177668
$937$	−46.5580	−1.52098	−0.760492	−	0.649347i	$-0.775042\pi$
$937$	−46.5580	−1.52098	−0.760492	+	0.649347i	$0.775042\pi$
$938$	−45.7423	−1.49354
$939$	−9.30396	−0.303623
$940$	11.7497	0.383232
$941$	6.32792	0.206284	0.103142	−	0.994667i	$-0.467110\pi$
$941$	6.32792	0.206284	0.103142	+	0.994667i	$0.467110\pi$
$942$	−112.305	−3.65908
$943$	−8.94164	−0.291180
$944$	−109.851	−3.57536
$945$	−8.71843	−0.283611
$946$	2.67122	0.0868487
$947$	−44.3781	−1.44209	−0.721047	−	0.692886i	$-0.756339\pi$
$947$	−44.3781	−1.44209	−0.721047	+	0.692886i	$0.756339\pi$
$948$	54.3338	1.76468
$949$	0.838036	0.0272038
$950$	−92.2963	−2.99449
$951$	−79.2958	−2.57134
$952$	33.7998	1.09546
$953$	−26.2801	−0.851296	−0.425648	−	0.904889i	$-0.639954\pi$
$953$	−26.2801	−0.851296	−0.425648	+	0.904889i	$0.639954\pi$
$954$	80.9687	2.62146
$955$	−17.3981	−0.562990
$956$	−44.9611	−1.45415
$957$	−23.1979	−0.749882
$958$	68.8732	2.22519
$959$	3.24461	0.104774
$960$	43.2968	1.39740
$961$	4.36281	0.140736
$962$	−2.53791	−0.0818254
$963$	58.0497	1.87063
$964$	38.0887	1.22675
$965$	2.57659	0.0829433
$966$	147.704	4.75230
$967$	42.2745	1.35946	0.679728	−	0.733465i	$-0.262098\pi$
$967$	42.2745	1.35946	0.679728	+	0.733465i	$0.262098\pi$
$968$	−8.37532	−0.269193
$969$	−22.0932	−0.709737
$970$	15.8910	0.510230
$971$	−26.9582	−0.865129	−0.432564	−	0.901603i	$-0.642391\pi$
$971$	−26.9582	−0.865129	−0.432564	+	0.901603i	$0.642391\pi$
$972$	−110.980	−3.55970
$973$	75.9746	2.43563
$974$	61.5941	1.97360
$975$	−1.80216	−0.0577153
$976$	74.2224	2.37580
$977$	30.4031	0.972682	0.486341	−	0.873769i	$-0.338331\pi$
$977$	30.4031	0.972682	0.486341	+	0.873769i	$0.338331\pi$
$978$	−109.334	−3.49611
$979$	−3.38193	−0.108087
$980$	45.2762	1.44629
$981$	−70.6379	−2.25530
$982$	−1.58345	−0.0505299
$983$	30.5554	0.974566	0.487283	−	0.873244i	$-0.337988\pi$
$983$	30.5554	0.974566	0.487283	+	0.873244i	$0.337988\pi$
$984$	37.5400	1.19673
$985$	−19.0143	−0.605847
$986$	−23.6447	−0.753001
$987$	−25.4881	−0.811297
$988$	−7.26340	−0.231079
$989$	5.22814	0.166245
$990$	9.81013	0.311786
$991$	−3.75012	−0.119127	−0.0595633	−	0.998225i	$-0.518971\pi$
$991$	−3.75012	−0.119127	−0.0595633	+	0.998225i	$0.518971\pi$
$992$	−92.6196	−2.94068
$993$	−44.0175	−1.39685
$994$	−124.814	−3.95887
$995$	16.8281	0.533486
$996$	−103.616	−3.28319
$997$	49.4156	1.56501	0.782504	−	0.622645i	$-0.213942\pi$
$997$	49.4156	1.56501	0.782504	+	0.622645i	$0.213942\pi$
$998$	40.4553	1.28059
$999$	12.8859	0.407690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.g.1.4	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.g.1.4	✓	69	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.67122 q^{2} +2.62074 q^{3} +5.13539 q^{4} +0.949400 q^{5} -7.00056 q^{6} -4.03564 q^{7} -8.37532 q^{8} +3.86827 q^{9} +O(q^{10})\)	\(q-2.67122 q^{2} +2.62074 q^{3} +5.13539 q^{4} +0.949400 q^{5} -7.00056 q^{6} -4.03564 q^{7} -8.37532 q^{8} +3.86827 q^{9} -2.53605 q^{10} -1.00000 q^{11} +13.4585 q^{12} +0.167776 q^{13} +10.7801 q^{14} +2.48813 q^{15} +12.1015 q^{16} +1.00000 q^{17} -10.3330 q^{18} -8.43016 q^{19} +4.87554 q^{20} -10.5764 q^{21} +2.67122 q^{22} +5.22814 q^{23} -21.9495 q^{24} -4.09864 q^{25} -0.448166 q^{26} +2.27550 q^{27} -20.7246 q^{28} +8.85167 q^{29} -6.64633 q^{30} +5.94666 q^{31} -15.5751 q^{32} -2.62074 q^{33} -2.67122 q^{34} -3.83144 q^{35} +19.8651 q^{36} +5.66287 q^{37} +22.5188 q^{38} +0.439697 q^{39} -7.95152 q^{40} -1.71029 q^{41} +28.2517 q^{42} +1.00000 q^{43} -5.13539 q^{44} +3.67253 q^{45} -13.9655 q^{46} +2.40992 q^{47} +31.7148 q^{48} +9.28639 q^{49} +10.9484 q^{50} +2.62074 q^{51} +0.861596 q^{52} -7.83596 q^{53} -6.07835 q^{54} -0.949400 q^{55} +33.7998 q^{56} -22.0932 q^{57} -23.6447 q^{58} -9.07751 q^{59} +12.7775 q^{60} +6.13333 q^{61} -15.8848 q^{62} -15.6109 q^{63} +17.4014 q^{64} +0.159287 q^{65} +7.00056 q^{66} -4.24323 q^{67} +5.13539 q^{68} +13.7016 q^{69} +10.2346 q^{70} -11.5783 q^{71} -32.3980 q^{72} +4.99497 q^{73} -15.1267 q^{74} -10.7415 q^{75} -43.2922 q^{76} +4.03564 q^{77} -1.17453 q^{78} +4.03713 q^{79} +11.4892 q^{80} -5.64131 q^{81} +4.56855 q^{82} -7.69890 q^{83} -54.3137 q^{84} +0.949400 q^{85} -2.67122 q^{86} +23.1979 q^{87} +8.37532 q^{88} +3.38193 q^{89} -9.81013 q^{90} -0.677084 q^{91} +26.8486 q^{92} +15.5846 q^{93} -6.43741 q^{94} -8.00359 q^{95} -40.8181 q^{96} -6.26604 q^{97} -24.8059 q^{98} -3.86827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9}+O(q^{10}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9	\( 69 q - 11 q^{2} - 3 q^{3} + 65 q^{4} - 6 q^{5} - 10 q^{6} - 11 q^{7} - 33 q^{8} + 56 q^{9} - q^{10} - 69 q^{11} - 3 q^{12} - 28 q^{13} - 15 q^{14} - 45 q^{15} + 53 q^{16} + 69 q^{17} - 17 q^{18} - 32 q^{19} - 21 q^{20} - 38 q^{21} + 11 q^{22} - 41 q^{23} - 11 q^{24} + 67 q^{25} - 6 q^{26} - 3 q^{27} - 21 q^{28} - 22 q^{29} - 22 q^{30} - 27 q^{31} - 87 q^{32} + 3 q^{33} - 11 q^{34} - 44 q^{35} + 59 q^{36} + 24 q^{37} - 22 q^{38} - 59 q^{39} + q^{40} - 43 q^{41} - 15 q^{42} + 69 q^{43} - 65 q^{44} - 12 q^{45} - 21 q^{46} - 99 q^{47} + 2 q^{48} + 64 q^{49} - 78 q^{50} - 3 q^{51} - 57 q^{52} - 50 q^{53} + 20 q^{54} + 6 q^{55} - 59 q^{56} - 15 q^{57} + 22 q^{58} - 82 q^{59} - 86 q^{60} - 24 q^{61} + 15 q^{62} - 63 q^{63} + 63 q^{64} - 23 q^{65} + 10 q^{66} - 54 q^{67} + 65 q^{68} + 36 q^{69} + 9 q^{70} - 128 q^{71} - 69 q^{72} + 2 q^{73} - 58 q^{74} - 31 q^{75} - 76 q^{76} + 11 q^{77} - 19 q^{78} - 43 q^{79} - 19 q^{80} + 49 q^{81} - 2 q^{82} - 62 q^{83} - 82 q^{84} - 6 q^{85} - 11 q^{86} - 62 q^{87} + 33 q^{88} - 49 q^{89} - 37 q^{90} - 2 q^{91} - 96 q^{92} - 29 q^{93} - 75 q^{94} - 133 q^{95} - 86 q^{96} + 5 q^{97} - 72 q^{98} - 56 q^{99}+O(q^{100}) \) 69 * q - 11 * q^2 - 3 * q^3 + 65 * q^4 - 6 * q^5 - 10 * q^6 - 11 * q^7 - 33 * q^8 + 56 * q^9 - q^10 - 69 * q^11 - 3 * q^12 - 28 * q^13 - 15 * q^14 - 45 * q^15 + 53 * q^16 + 69 * q^17 - 17 * q^18 - 32 * q^19 - 21 * q^20 - 38 * q^21 + 11 * q^22 - 41 * q^23 - 11 * q^24 + 67 * q^25 - 6 * q^26 - 3 * q^27 - 21 * q^28 - 22 * q^29 - 22 * q^30 - 27 * q^31 - 87 * q^32 + 3 * q^33 - 11 * q^34 - 44 * q^35 + 59 * q^36 + 24 * q^37 - 22 * q^38 - 59 * q^39 + q^40 - 43 * q^41 - 15 * q^42 + 69 * q^43 - 65 * q^44 - 12 * q^45 - 21 * q^46 - 99 * q^47 + 2 * q^48 + 64 * q^49 - 78 * q^50 - 3 * q^51 - 57 * q^52 - 50 * q^53 + 20 * q^54 + 6 * q^55 - 59 * q^56 - 15 * q^57 + 22 * q^58 - 82 * q^59 - 86 * q^60 - 24 * q^61 + 15 * q^62 - 63 * q^63 + 63 * q^64 - 23 * q^65 + 10 * q^66 - 54 * q^67 + 65 * q^68 + 36 * q^69 + 9 * q^70 - 128 * q^71 - 69 * q^72 + 2 * q^73 - 58 * q^74 - 31 * q^75 - 76 * q^76 + 11 * q^77 - 19 * q^78 - 43 * q^79 - 19 * q^80 + 49 * q^81 - 2 * q^82 - 62 * q^83 - 82 * q^84 - 6 * q^85 - 11 * q^86 - 62 * q^87 + 33 * q^88 - 49 * q^89 - 37 * q^90 - 2 * q^91 - 96 * q^92 - 29 * q^93 - 75 * q^94 - 133 * q^95 - 86 * q^96 + 5 * q^97 - 72 * q^98 - 56 * q^99

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